7333
J. Phys. Chem. 1989, 93, 7333-7335 modes correspond to distortions of the separated XH3 and SnH3 groups. Values of force constants and vibrational frequencies of XH3 groups are similar to that found on the XzH6 compounds. With regard to the Sn-X stretch force constants and associated frequencies, it can be seen that they decrease monotonically on going from X = C cfsnx = 2.269 mdyn/A, w5 = 576 cm-’) to X = Sn CfSn-Sn = 1.322 mdyn/A, o5= 192 cm-I). It is obvious that this evolution of force constants is responsible of the progressive destabilization of the Sn-X bond and of the higher instability of distannane with respect to the methylstannane.
Conclusions In this work we have carried out ab initio calculations on a series of molecules SnH3XH3 (X = C, Si, Ge, Sn). With regard to distannane, we have shown that is an ethane-like compound with D3dsymmetry. Our predicted tin-tin bond distance (2.804 A) is in reasonably good agreement with experimental value found in hexaphenyldistannane (2.79 A). The force constant associated with the tin-tin stretch (1.282 mdyn/A) is quite small, indicating a weak metal-metal bond. These results together with the small
torsional force constant (0.012 m d y d ) and the very low rotational barrier (0.39 kcal-mol-’) seem to suggest that molecular structure of distannane can be understood as two weakly COMected stannyl groups with near free rotation around the tin-tin bond and poor interaction. Calculated harmonic frequencies and infrared intensities agree qualitatively with available experimental data (solid sample) and we have argued for an alternative assignment of the bands at 690 and 880 cm-’, although further experimental work (mainly Raman) is encouraged. Comparing distannane with SnH3XH3molecules, we have shown that on going from X = C to X = Sn, the Sn-X bond distance increases whereas fsn-x stretch force constants and rotational barriers decrease, all together revealing a progressive loss of bond strength. Acknowledgment. This work was supported by the Direccion General de Investigacion Cientifica y Tecnica (PB86-0140). We are grateful to Dr. C. Pouchan for helpful discussions and a referee for valuable comments. Registry No. SnH,SnH,, 32745-15-6; GeH,SnH,, 15118-47-5; SiH,SnH,, 14450-86-3; CH3SnH3,1631-78-3; Sn, 7440-31-5.
A New Electronegativity Scale. 8. Correlatlon of the Ionization Potentials of the Main-Group Atoms (I-VI I) Yu-Ran Luo* and Sidney W. Benson Donald P. and Katherine B. Loker Hydrocarbon Research Institute, Department of Chemistry, University of Southern California, University Park, Los Angeles, California 90089-1 661 (Received: February 6, 1989; In Final Form: May 22, 1989)
Linear correlations are found to exist between the ionization potentials of the seven main-group elements (I-VII) and four different measures of their electronegativity. The electronegativity scales tested are the Pauling scale, xp, a modification xp2,the Allred-Rochow scale, xA, and our recently proposed scale Vx. The latter gives a fit for all main-group elements with an average deviation of 0.14 eV and a root-mean-square deviation of 0.16 eV. The other three scales give fits that show larger deviations by factors of about 2. The maximum deviation with Vx are 0.45 and 0.35 eV for Bi and Pb, respectively. These along with T1 may show anomalies relative to the lighter elements. By use of the correlations, estimates are made of the covalent radii of Ra and Po and the IP of Fr and At.
Introduction Over 20 years ago, the unshielded core potential of atom X, Vx = nx/rx, where nx is the number of valence electrons in the bonding atom X and rx (A) is its covalent radius, was proposed as the basis for a new electronegativity scale by Yuan.’ However, no one including Yuan has since attempted to use Vx for the estimation or correlation of physical properties. Recently we have found that Vx can be quantitatively correlated with heats of formation, bond dissociation energies, and the group parameters of polyatomic molecules in homologous series?+ These properties correlate only qualitativelyg with the more traditional electro(1) Yuan, H. C. Acta Chim. Sin. 1964, 30, 341. (2) Luo, Y. R.; Benson, S.W. J . Phys. Chem. 1988, 92, 5255. (3) Luo, Y. R.; Benson, S.W. J . Am. Chem. SOC.1989, 1 1 1 , 2480. (4) Luo, Y. R.; Benson, S. W. J . Phys. Chem. 1989, 93, 3304. (5) Luo, Y. R.; Benson, S. W. J . Phys. Chem. 1989, 93, 3306. (6) Luo, Y. R.; Benson, S.W. J . Phys. Chem. 1989, 93, 1674. (7) Luo, Y. R.; Benson, S.W. J . Phys. Chem. 1989, 93, 4643. (8) Luo, Y. R.; Benson, S.W. J . Phys. Chem. 1989, 93, 3791. (9) Luo, Y.R.; Benson, S. W. J. Phys. Chem. Submitted for publication 1989.
0022-365418912093-7333$01.50/0
TABLE I: Slopes and Intercepts for the Linear Corrclations of V x with IP for Main Grouas I-VI1 (See Ea 1)
group I I1 111
IV V
VI VI1
slope“
intercept/eV
4.83 f 0.29 3.70 f 0.19 1.62 f 0.14 1.57 f 0.10 2.05 f 0.10 1.26 f 0.05 1.62 f 0.05
1.86 f 0.18 1.74 f 0.27 2.29 f 0.39 2.97 f 0.35 1.0 f 0.45 3.34 f 0.32 1.85 f 0.32
“If we put V, in units of energy, then the slopes are dimensionless. negativity scales, such as Pauling’s,Io Mulliken’s,’ l * I 2 AllredRochow’s,13 and others. The unshielded core potential, Vx,is a very simply calculated property of atom X. Vx although derived for atoms has been also ~~
(10) Pauling, L. The Nature of the Chemical Bond, 3rd ed.: Cornell University Press: Ithaca, New York, 1960. (1 1) Mulliken, R. S. J . Chem. Phys. 1934, 2, 782. (12) Mulliken, R. S. J. Chem. Phys. 1935, 3, 573. (13) (a) Allred, A. L.;Rochow, E. G. J. Inorg. Nucl. Chem. 1958,5,264, 269. (b) Ibid. 1961, 17, 215. 0 . 1989 American Chemical Societv
7334 The Journal of Physical Chemistry, Vol. 93, No. 21, 1989
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Luo and Benson
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Figure 1. Relation between Vx and first IP for groups I, IV, and VI.
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Figure 2. Relation between Vx and IP for groups I1 and V.
applied to groups in molecules where X = OH, NH2, CH3, etc. Substitutional effects will be discussed in later publications where the substitutions are replacements for H on the polyvalent atom X. The quantity of Vxe2where c is the electronic charge has the dimensions of energy and may be expected to correlate with energetic properties of groups in molecules, radicals, and ions. Ionization potentials (IP) are one of the most important properties of atoms and should be expected to correlate with measures of electronegativity. These relations are explored here. Correlations of Ionization Potential (IP) and Electronegativity
Pauling's original scale for electronegativity, xp,was based on the heats of formation of diatomic molecules in the gas state from elements in the gas state. Originally this could only be done for the monovalent elements of groups I and VII'O but was later extended to polyvalent atoms generally by making use of "average bond energies". We found it to give only qualitative correlation of differences in A f P of MH, and M(CH3), (AAfHo[MH,/M(CH3)"]) and AAfP[M(CH3),/M(C2H5)n].14 This is not entirely unexpected since x p has the dimensions of (energy)'I2 while it is xp2that has the units of energy. Mulliken's scale x,,, would be anticipated to give a better correlation. It has the dimensions of energy and is derived from the ionization potentials and the electron affinities of the elements. Allred's electronegativity scale xA is proportional to the force on a valence electron and thus also (14) Benson, S.W.; Francis, J.; Tsotsis, T. J . Phys. Chem. 1988,92,4515.
Figure 3. Relation between Vx and IP for groups 111 and VII. TABLE II: Average Deviation, Maximum Deviation, and Root-Mean-Square Deviation for Best Linear Correlations of IP and Four Electronegativity Scales measure groups of fit" XP XP2 XA vX I av 0.12 0.11 0.16 0.06 rms 0.14 0.14 0.21 0.08 max 0.22 0.25 0.26 0.13 I1 av 0.15 0.22 0.14 0.16 rms 0.18 0.25 0.14 0.17 max 0.29 0.46 0.19 0.26 111 av 0.50 0.47 0.49 0.17 rms 0.54 0.51 0.60 0.18 max 0.68 0.66 1.00 0.26 IV av 0.26 0.26 0.52 0.18 rms 0.30 0.30 0.57 0.21 max 0.45 0.45 0.97 0.35 V av 0.60 0.64 0.41 0.24 rms 0.75 0.81 0.49 0.26 max 1.30 1.34 0.84 0.45 VI av 0.11 0.15 0.24 0.13 rms 0.12 0.19 0.31 0.15 max 0.14 0.30 0.61 0.23 VI1 av 0.05 0.13 0.28 0.13 rms 0.06 0.16 0.33 0.15 max 0.10 0.25 0.5 0.25 Deviations reported in eV.
TABLE III: Average and rms Deviations of the Linear Correlations between All Main-Group Elements for Four Electronegativity Scales av error/eV rms error/eV
XP
XP2
XA
VX
0.26 0.30
0.29 0.34
0.32 0.38
0.14 0.16
might not be expected to show quantitative correlation with energy-related properties. We have explored the correlation of the first IP of the maingroup elements with Vx,xp, and xA. The results for Vx are presented in Figures 1-3. They can be represented by (1). IP(eV) = SV,
(A-1) + i
(1)
In Table I we list the slopes s and intercepts i of the straight lines drawn through the data of Figures 1-3. Similar correlations have been made of the other measures of electronegativity xp,xp2, and xA against IP. We omit the resultant graphs but summarize the results of least mean square fits of all four scales in Table 11. Listed in Table I1 are the average deviations, root-mean-square deviations, and the maximum deviations of the linear correlations. It can be seen that for most groups all scales give reasonable correlation. For groups 111, IV, and V, however, the results for
Ionization Potentials of the Main-Group Atoms
The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 7335
TABLE IV: The Electronegativity Scales and Ionization Potentials for Atoms of Main Groups group atom X xpa xAb V,C r;/A IPd/eV I 2.1 (2.20)c 2.70 0.3707 13.596 H 1.0 0.97 0.75 1.337 5.392 Li 1.539 5.139 0.9 1.01 0.65 Na 1.953 4.341 0.8 0.91 0.51 K 4.177 2.087 0.8 0.89 0.48 Rb 3.894 2.323 cs 0.7 0.86 0.43 2.40 (3.98) 0.7 0.86 0.42 Fr 0.96 0.322 1.5 1.47 2.08 Be I1 7.646 1.30 1.2 1.23 1.54 Mg 1.74 6.113 1.0 1.04 1.15 Ca 1.91 5.695 1.0 0.99 1.05 Sr 1.98 5.212 0.9 0.97 1.01 Ba 5.279 0.9 0.97 (0.96) (2.09) Ra 0.82 2.0 2.01 3.66 8.298 B 111 1.248 5.986 1.5 1.47 2.40 A1 1.26 5.999 Ga 1.6 1.82 2.38 1.497 5.786 1.7 1.49 2.00 In 6.108 1.8 1.07 TI 0.771 1 1.260 C 2.5 2.50 5.19 IV 1.173 8.151 1.8 1.74 3.41 Si 1.223 1.8 2.02 3.24 7.899 Ge 1.412 1.8 1.72 2.83 7.344 Sn 7.416 1.55 1.8 1.55 2.60 Pb 14.534 0.75 V 3.0 3.07 6.67 N 1.10 2.1 2.06 4.55 10.486 P 1.19 9.81 As 2.0 2.20 4.20 1.38 1.9 1.82 3.62 8.641 Sb 1.52 7.289 Bi 1.9 1.67 3.29 0.74 3.5 3.50 8.11 13.618 VI 0 1.04 2.5 2.44 5.77 10.360 S 1.17 9.752 2.4 2.48 5.13 Se 1.37 2.1 2.01 4.38 9.009 Te 8.42 2.0 1.76 (4.03) (1.49) Po 0.706 F 4.0 4.10 9.915 17.967 VI1 0.994 3.0 2.83 7.04 12.967 c1 11.814 1.141 Br 2.8 2.74 6.13 1.333 2.5 2.21 5.25 10.451 I 1.50 2.4 1.90 4.67 (9.42) At
deviations of IP versus electronegativity. We note that the Vx correlation has deviations about a factor of 2 better than that found with the other three scales. Finally, in Table IV we list the covalent radii (A) and the IP (eV) used in making the present correlations.
‘Pauling scale, from ref 10. bAllred-Rochow scale, from ref 13a. CThe covalent radii of the diatomic molecules, X2,in the table are taken from the bond lengths measured by molecular spectra.I5 This applies only to the monovalent elements of groups I and VII. The other values are from ref 16-18. dFrom ref 19. CFrom thermochemical data, see ref 13b.
Registry No. Radium, 7440-14-4; polonium, 7440-08-6; francium, 7440-73-5; astatine, 7440-68-8.
~
Vx are considerably better than for the other measures of electronegativity . In Table 111 we make an average Over all Seven main-group elements (I-VII) of the average deviation and root-mean-square
Discussion All four electronegativity scales give some more or less reasonable linear fit with the first IP of the main-group elements. However, the results with Vx are significantly better, overall by a factor of about 2. However, the maximum deviations are the most sensitive measure, and here Vx provides a better fit by about a factor of 3 or more. Its average deviation (Table 111) for all seven groups is only 0.14 eV. Its maximum deviation of 0.45 eV for Bi (group V) occurs only once and is sufficiently unique to make us question the reliability of the listed IP(Bi). An increase in the latter of about 0.5 eV would remove this large deviation (Figure 2). The second largest deviation of 0.35 eV is found for Pb and is in the opposite sense to that found for Bi. On a relative basis the average deviations relative to the ionization potentials of the elements are less than 1%. This is a quite unexpected result but very useful. Using the linear parameters given in Table I, we can estimate covalent radii or Vx for unknown main-group elements if their IPS are known. Conversely if their IPS are known or can be estimated, then it is possible to estimate values for Vx and hence of rx, the covalent radius. Values estimated in this way are shown in parentheses in Table IV for Fr (group I), Ra (group 11), Po (group VI), and At (group VII). There does not appear to be reliable data on the value of rx for T1, but its IP would place it in an anomalously high position on the graph shown in Figure 3. This suggests that for the subgioup IIIB the IP may be anomalous in this last row of the periodic table. Gold of group IB has an anomalously high IP. Acknowledgment. This work has been supported by a grant from the National Science Foundation (CHE-8714647).
(15) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules: VNR. New York. * . 1979. (16) Pauling, L. J. Am.-Chem. SOC.1947, 69,’542. (17) Little, E. J., Jr.; Jones, M. M. J. Chem. Educ. 1960, 37, 231. (18) Gordon, A. G.; Ford, R. A. A Chemist’s Companion: Handbook of Practical Data, Techniques, and References; Wiley: New York, 1973. (19) Benson, S. W. J. Phys. Chem. 1989, 93, 4457.
